The difficulty is the mentality that it broke because you used it correctly, instead of them understanding that-
it’s their kit, not yours.
Maintenance and faults are not the same as misuse and damage

The attitude is just deliberate stupidity.

A reasonable (in my opinion) response would be to get it sorted yourself, if you can. And then plan how that will be offset in the final bill, and how the deposit paid will be used to cover the last few weeks of residence. I’m pretty mercenary about this now, as our current landlord quickly learned not to piss about.
We paid for the aircon at our previous place, and brought it with us to the new apartment, as the previous occupant had stolen the compressor and blower unit. I think all in, it was $80 to uninstall and reinstall. But they used the existing hoses, and the system leaked down. $15 got a re-charge, but they didn’t do any investigation, and so it leaked down again. They’re aware of my thoughts regarding their skills…

I’ve little idea about domestic systems, but from what I know about vehicles, modern aircon gases are slightly more prone to leaking (especially in systems that may already be compromised) than older gases which were in use until the mid 90s. Wear on rotating parts, leaks in seals, etc. basic lack of maintenance, and poor installation in the first place. Systems that had sat dormant and seals have dried out.
Most re-charges will probably be just a gas. I’d imagine that to be done correctly, it would require a specific quantity of lubricating oil proportionate to the gas being added. The system would need to be run, and then checked for pressure. Simply connecting up the hoses and filling the system won’t cut it in a 20minute visit.
Certainly, this is the case for my cars, and the basic process must be similar.